MATH 704 Syllabus
Here is a preliminary list of the topics that I plan to discuss in the course, subject to revision:
- Weierstrass Product and Factorization Theorems
- Blaschke products and their zeros
- Order of an entire function, Hadamard's Factorization Theorem
- Rational and polynomial approximation
- Geometry in the hyperbolic plane, the Ahlfors-Schwarz Lemma
- Distortion theorems for conformal maps
- Length-area inequalities, conformal invariants
- Boundary behavior of conformal maps
- Non-tangential limits, theorems of Fatou and Riesz brothers
- Theorems of Picard and Bloch
- Holomorphic coverings and branched coverings
- Riemann surfaces and the Uniformization Theorem
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Math 704